Deep-buried tunnel microseismic monitoring method based on transformer time sequence model

Abstract

The present application mainly relates to the technical field of rock mass monitoring, in order to solve the problems of difficult identification of deep-buried tunnel microseismic signal and low positioning accuracy, the present application provides a deep-buried tunnel microseismic monitoring method based on a Transformer time sequence model, first, the microseismic monitoring signal obtained based on dynamic section migration is divided into data frames; then, a Transformer time sequence model is established by introducing the P-wave first arrival time as the phase prior bias; the trained model is used for event existence judgment, event classification and microseismic monitoring signal arrival time regression prediction on the data frame; the microseismic event frame is merged and fused through adaptive threshold judgment, and the complete microseismic event start and end time and confidence are obtained; finally, according to the confidence threshold, combined with the monitoring section sensor position, the improved particle swarm optimization algorithm is used to solve the microseismic event source position and energy, the microseismic event is accurately identified, and the false alarm and false alarm rates are reduced.

Description

Technical Field

[0001] This invention relates to the field of rock mass monitoring technology, and in particular to a microseismic monitoring method for deep-buried tunnels based on the Transformer time series model. Background Technology

[0002] As tunnel excavation depth increases, the tunnel face and surrounding rock are prone to dynamic disasters such as rock bursts under high ground stress. Efficient monitoring and timely early warning of microseismic events generated during deep-buried tunnel construction are crucial. Microseismic monitoring technology, as an active, non-contact monitoring method, can capture weak microseismic signals generated by internal rock fractures or deformations, enabling early warning of potential rock instability, rockbursts, and other disasters. However, the geological environment of deep-buried tunnels is complex, the stress field of the surrounding rock changes drastically, and the dynamic response of the rock mass is significant during tunnel face advancement. Traditional microseismic monitoring methods face numerous challenges in signal identification, event location, and energy inversion.

[0003] Existing solutions mostly employ single-plane or dual-plane sensor arrays around the tunnel, combined with least squares or genetic algorithms for seismic source location. However, once the tunnel has traveled a certain distance, the entire array needs to be relocated, leading to monitoring "window periods," response delays, and operational risks. In terms of data processing, reliance on fixed threshold triggers or manual screening is common, making it prone to missed detections / false alarms and hindering real-time risk assessment. These solutions exhibit the following drawbacks:

[0004] (1) Limited positioning accuracy: The monitoring capability decreases or the number of sensors is reduced during the sensor migration, resulting in insufficient information at that time;

[0005] (2) Dynamic response lag: Traditional overall translation requires waiting for tunneling to reach a fixed mileage, and the near-field signal-to-noise ratio deteriorates with increasing distance;

[0006] (3) High construction risks and costs: Frequent large-scale drilling and disassembly increase the probability of equipment damage from impact and the maintenance costs.

[0007] (4) Insufficient intelligent recognition: Fixed thresholds and empirical rules are difficult to adapt to complex noise and non-stationary microseismic monitoring signals, resulting in insufficient real-time performance and stability.

[0008] Therefore, there is an urgent need for a microseismic monitoring method for deep-buried tunnels that can integrate prior physical knowledge, adapt to dynamic monitoring scenarios, and possess high robustness and high precision, so as to achieve accurate identification, classification, location, and energy assessment of microseismic events and provide reliable technical support for engineering safety. Summary of the Invention

[0009] The technical problem to be solved by this invention is to provide a microseismic monitoring method for deep-buried tunnels based on the Transformer time series model, with the aim of improving the accuracy and efficiency of microseismic event monitoring.

[0010] The technical solution adopted by the present invention to solve the above-mentioned technical problems is as follows:

[0011] A microseismic monitoring method for deep-buried tunnels based on the Transformer time series model, the method comprising:

[0012] Step S1: Obtain microseismic monitoring signals based on the set monitoring sections, and divide the microseismic monitoring signals into different data frames according to the set window length and step size;

[0013] Step S2: Establish a Transformer time series model based on a multi-head attention mechanism, wherein the multi-head attention mechanism of the Transformer time series model includes a phase prior bias of the P-wave first arrival time obtained based on physical prior knowledge.

[0014] Step S3: Using data frames as input, train the Transformer time series model, and predict microseismic events based on the trained Transformer time series model.

[0015] Step S4: Merge and fuse the data frames identified as microseismic events to obtain the start and end times of the microseismic events;

[0016] Step S5: Based on the location of the monitoring section and the start and end times of the microseismic event, the source location and energy of the microseismic event are solved using an improved particle swarm optimization algorithm.

[0017] Furthermore, the monitoring section setting in step S1 includes: setting a near-field monitoring section, a mid-field monitoring section, and a far-field monitoring section behind the working face, and acquiring microseismic monitoring signals based on the set three-level monitoring sections. The near-field monitoring section is 10m-20m away from the working face, the mid-field monitoring section is 30m-50m away from the working face, and the far-field monitoring section is 60m-80m away from the working face.

[0018] Furthermore, step S1, which involves acquiring microseismic monitoring signals based on the set monitoring sections, includes: deploying sensors at the top, bottom, and left and right sides of the monitoring section, and using four sets of sensors in rotation to dynamically migrate the monitoring section to acquire microseismic monitoring signals by removing the original far-field monitoring section, upgrading the near-field monitoring section to a mid-field monitoring section, upgrading the mid-field monitoring section to a far-field monitoring section, and setting up a new near-field monitoring section.

[0019] Furthermore, the P-wave arrival time in step S2 is obtained based on the ratio of short-time average to long-time average.

[0020] Furthermore, the Transformer time series model output layer includes an event category classification head, a microseismic event existence output head, and a seismic phase arrival time regression head. The event existence output head is used to output the probability of microseismic events, the event category classification head is used to output the event category, and the seismic phase arrival time regression head is used to output the predicted arrival time of P-waves or S-waves.

[0021] The P-wave first arrival time is added to the Transformer time series model based on a multi-head attention mechanism to establish a biased attention weight matrix. This allows the model to determine the existence of microseismic event frames, the probability of microseismic events, and the prediction of P-waves or S-waves within the P-wave first arrival time range. The biased attention weight matrix is ​​as follows: , ,in, , , These are the query, key, and value matrices, respectively. For channel dimensions; The relative time error between the query and the key; For the index of the data frame; For the first The P-wave arrival time of each monitoring section; This is the tolerance for the P-wave first arrival time window; This represents the bias strength.

[0022] Furthermore, step S3, training the Transformer temporal model, includes:

[0023] The fused features, including the monitoring section location and data frame, are obtained through three-component channel attention fusion. , will integrate features Time coding and monitoring section location coding After being spliced ​​together, the data is used as input, and the presence or absence of an event in the corresponding data frame, the event type, and the arrival time of the P wave or S wave are used as the true labels to train the established Transformer time series model.

[0024] Based on the loss function during training The model training results are evaluated, and the model is optimized. The loss function is: , ;in, , , and These are the weighting coefficients; It is a binary cross-entropy, used to determine whether a microseismic event has occurred; For real labels, This indicates that an event exists. This indicates that the event does not exist; The probability of the event predicted by the model. When an event exists =1, otherwise =0; As an indicator function, multi-class cross-entropy is computed only on frames where events occur; For the actual label of the event type; Indexed by event category; The probability distribution of event types predicted by the model; For Huber's losses; and For the arrival times of the P-wave and S-wave predicted by the model; and These are the actual arrival labels for P-wave and S-wave, respectively. For safe phase spacing, ; The category traversal index is used in the summation formula; The logit vector of the classification head; For the first The logit value of the event class; For temperature parameters; This represents the total number of event categories.

[0025] Furthermore, step S4, which involves merging and fusing data frames identified as microseismic events, includes:

[0026] Estimating dynamic noise using sliding window MAD and providing a threshold , When the probability of microseismic events in the data frame Greater than Then the data frame is marked as a microseismic event frame, where, The median; This is a sliding window sequence used for threshold estimation; For noise scaling estimation; Sliding window mean; This is the threshold coefficient; This represents the threshold for microseismic events.

[0027] Merge consecutively labeled microseismic event frames into a complete microseismic event, and calculate the summation classification probability of the microseismic events: , , ,in, A collection of data frames; For indexing data frames; This is the weighted overall probability that the entire event belongs to category c; For the first category The probability of; For the first Frame weights; To adjust the parameters; For data frames The probability of belonging to category c; For data frames Signal-to-noise ratio; The event category for the final output; The confidence level of the event.

[0028] Furthermore, the method for obtaining the earthquake source location in step S6 is as follows: For confirmed microseismic events, a set of nonlinear equations for the earthquake source is constructed using the time difference between the arrival and departure of the microseismic monitoring signals. ,in, For the first One microseismic signal monitoring location; Location of the epicenter; For the first The time it takes for a microseismic signal monitoring station to receive a microseismic monitoring signal; This represents the start time of the microseismic event. The propagation velocity of the P-wave is given; the source nonlinear equations are solved using an improved particle swarm optimization algorithm to obtain the source distance. .

[0029] Furthermore, the objective function of the improved particle swarm optimization algorithm is: ,in, This represents the start time of the microseismic event. For the first The time it takes for a microseismic monitoring location to receive a microseismic monitoring signal; The number indicating the location of the microseismic signal monitoring; This represents the total number of locations monitored by microseismic signals.

[0030] Furthermore, the calculation method for microseismic energy in step S6 is as follows: ,in, For micro-vibration energy, Density of the surrounding rock; For the transmission speed of microseismic monitoring signals; Distance from the epicenter; The time span of the microseismic monitoring signal; This represents the displacement function of the microseismic monitoring signal at the monitoring location.

[0031] The beneficial effects of this invention are:

[0032] (1) A Transformer time series model with phase prior bias was established and combined with a multi-task joint loss function, which significantly enhanced the ability to identify microseismic events. It can still accurately identify weak signals under low signal-to-noise ratio conditions and effectively reduce the false alarm and false alarm rates.

[0033] (2) By using the dynamic rotation and migration mechanism of the microseismic signal monitoring sensor array, the monitoring gap caused by relocation in the traditional deployment method is eliminated, ensuring full and seamless coverage of the tunnel excavation process. Moreover, the rotation and migration only adds and removes the far-end section, reducing equipment wear and construction interference by fewer drilling and deployment operations.

[0034] (3) The source localization method based on the improved particle swarm optimization algorithm, combined with the multi-dimensional time constraints provided by the three-dimensional spatial envelope layout, can achieve stable and high-precision source localization and energy inversion in complex noise environments. Attached Figure Description

[0035] Figure 1 This is a flowchart of the microseismic monitoring method for deep-buried tunnels based on the Transformer time series model described in this invention;

[0036] Figure 2 This is a schematic diagram of the layout of the three-level monitoring area;

[0037] Figure 3 This is a schematic diagram showing the sensor locations on the monitoring cross-section. Detailed Implementation

[0038] The core of the technical solution of this invention to solve the above-mentioned technical problems is as follows: First, the microseismic monitoring signal is divided into multiple data frames according to a set time window and step size; a phase prior bias based on the P-wave first arrival time obtained from physical prior knowledge is added to the Transformer time series model to train the Transformer time series model, so that the model focuses on detecting microseismic events in the data frames within the P-wave first arrival time range during training and use; the trained model is used to determine the existence of events, classify events, and perform regression prediction of the arrival time of microseismic monitoring signals on the data frames; after determining that the data frame is a microseismic data frame, neighboring data frames are merged and fused to obtain the complete start and end time and confidence of the microseismic event; finally, based on the set confidence threshold, the location of the microseismic event source and the microseismic energy are solved using an improved particle swarm optimization algorithm based on the location of the monitoring section sensor and the start and end time of the microseismic event.

[0039] like Figure 1 As shown, the microseismic monitoring method for deep-buried tunnels based on the Transformer time series model of the present invention includes the following steps.

[0040] Step S1: Acquire microseismic monitoring signals.

[0041] Sensors are set at different locations on the monitoring section to acquire microseismic monitoring signals inside the tunnel, and the microseismic monitoring signals are divided into different data frames according to the set window length and step size.

[0042] As a preferred option, to improve the signal-to-noise ratio of the measured microseismic monitoring signal and significantly reduce the source location error, three levels of monitoring sections—near-field (10m–20m), mid-field (30m–50m), and far-field (60m–80m)—are sequentially arranged behind the tunnel face. For example... Figure 2 As shown, four sets of sensors are used in rotation. The monitoring sections are dynamically migrated by removing the original far-field monitoring section, upgrading the original near-field monitoring section to a new mid-field monitoring section, upgrading the original mid-field monitoring section to a new far-field monitoring section, and setting up a new near-field monitoring section. This satisfies the requirements of portability and redundancy under the conditions of tunnel face advancement.

[0043] As a further preferred option, such as Figure 3 As shown, four three-component sensors are evenly arranged at the top, bottom, and left and right sides of each monitoring section to form a three-dimensional spatial envelope, which further improves the ability to acquire the arrival time and azimuth information of microseismic monitoring signals in the tunnel and the positioning stability.

[0044] After preprocessing the collected microseismic monitoring signals, such as trend analysis, bandpass filtering, and gain normalization, they are divided into multiple data frames according to the set time window and step size.

[0045] Step S2: Establish a Transformer temporal model based on a multi-head attention mechanism.

[0046] The Transformer time series model output layer includes an event existence output head, an event category classification head, and a seismic phase arrival time regression head. The event existence output head is used to output the probability of microseismic events. The event category classification head is used to output the event category. In this invention, the event category classification head mainly includes four types of results: microseismic events, blasting events, mechanical noise, and surrounding rock disturbance. The seismic phase arrival time regression head is used to output the predicted arrival time of P-waves or S-waves.

[0047] The multi-head attention mechanism of the Transformer time series model also includes a phase prior bias based on the P-wave first arrival time obtained from prior physical knowledge. The purpose is to ensure that the phase arrival time regression head only considers time points that conform to the physical laws of P-wave propagation when analyzing microseismic time arrival times, so that the model focuses on the P-wave first arrival time range, effectively reducing false alarms and data processing volume.

[0048] Specifically, a biased attention weight matrix is ​​established. , This allows the Transformer time series model to consider only time points that conform to the physical laws of P-wave propagation when analyzing microseismic events, focusing the model on the first arrival time range of P-waves. This effectively reduces false alarms and data processing load. (The formula is incomplete.) , , These are the query, key, and value matrices, respectively. For channel dimensions; The relative time error between the query and the key; For the index of the data frame; For the first The P-wave arrival time of each monitoring section; The tolerance for the first arrival time window of the P-wave. This represents the bias strength.

[0049] The P-wave arrival time range is obtained based on the robust energy ratio (STA short-time average / LTA long-time average ratio).

[0050] Step S3: Using data frames as input, train the Transformer time series model, and predict microseismic events based on the trained Transformer time series model. A fused feature including the monitoring section location and the data frame is obtained through three-component channel attention fusion. , will integrate features Time coding and monitoring section location coding After being spliced ​​together, the data is used as input, and the presence or absence of an event in the corresponding data frame, the event type, and the arrival time of the P wave or S wave are used as the true labels to train the established Transformer time series model.

[0051] Based on the loss function during training The model training results are evaluated, and the model is optimized. The loss function is: , ,in, , , and These are the weighting coefficients; It is a binary cross-entropy, used to determine whether a microseismic event has occurred; For real labels, This indicates that an event exists. This indicates that the event does not exist; The probability of the event predicted by the model. When an event exists =1, otherwise =0; As an indicator function, multi-class cross-entropy is computed only on frames where events occur; For the actual label of the event type; Indexed by event category; The probability distribution of event types predicted by the model; For Huber's losses; and For the arrival times of the P-wave and S-wave predicted by the model; and These are the actual arrival labels for P-wave and S-wave, respectively. For safe phase spacing, ; The category traversal index is used in the summation formula; The logit vector of the classification head; For the first The logit value of the event class; For temperature parameters; This represents the total number of categories.

[0052] Step S4: Merge and fuse the data frames identified as microseismic events to obtain the start and end times and confidence levels of the microseismic events.

[0053] Based on the trained Transformer time series model, the presence and type of events in predicted data frames, as well as the arrival time of P-waves or S-waves, are used to merge and fuse data frames identified as microseismic events. Specifically, this includes:

[0054] Estimating dynamic noise using sliding window MAD and providing a threshold , When the probability of microseismic events in the data frame Greater than Then the data frame is marked as a microseismic event frame, where, The median; This is a sliding window sequence used for threshold estimation; For noise scaling estimation; Sliding window mean; This is the threshold coefficient; This represents the threshold for microseismic events.

[0055] Merge consecutively labeled microseismic event frames into a complete microseismic event, and calculate the summation classification probability of the microseismic events: , , ,in, A collection of data frames; For indexing data frames; This is the weighted overall probability that the entire event belongs to category c; For the first category The probability of; For the first Frame weights; To adjust the parameters; For data frames The probability of belonging to category c; For data frames Signal-to-noise ratio; The event category for the final output; The confidence level of the event.

[0056] Step S5: Based on the set confidence threshold, and using the location of the monitoring section sensor group and the start and end times of the microseismic event, solve the source location and energy of the microseismic event using an improved particle swarm optimization algorithm.

[0057] For confirmed microseismic events, a set of nonlinear source equations is constructed using the arrival time difference of microseismic monitoring signals from multiple monitoring sections: ,in, For the first The location of the microseismic signal monitoring point, i.e., the sensor location; Location of the epicenter; For the first The time it takes for a microseismic signal monitoring station to receive a microseismic monitoring signal; This represents the start time of the microseismic event. The propagation velocity of the P-wave is used; the onset time of the microseismic event is obtained by solving the nonlinear equations of the seismic source based on an improved particle swarm optimization algorithm. The optimal value is then used to obtain the distance to the epicenter. .

[0058] Improved Particle Swarm Optimization (IPSO) Global-Local Cooperative Solution: To avoid sensitivity to local extrema and poor initial conditions, this invention employs an improved particle swarm optimization approach for global optimization, coupled with refined local iterations. IPSO introduces the following on top of basic PSO: (a) chaotic sequence initialization to enhance population diversity; (b) dynamic inertia weights and adaptive learning factors to balance global exploration and local exploitation; (c) elite retention and perturbation to prevent premature convergence; and (d) a multi-objective cost function. This represents the start time of the microseismic event. For the first The time it takes for each microseismic monitoring location to receive a microseismic monitoring signal. The number represents the location of the microseismic signal monitoring, which is based on the minimum mean square residual at the time of arrival, and may also be weighted to consider geometric distribution constraints or amplitude consistency terms.

[0059] Based on the solved focal distance Calculating microseismic energy The micro-vibration energy The calculation method is as follows: ,in: Density of the surrounding rock; Wave speed; Distance from the epicenter; The time span of the microseismic monitoring signal; This is the displacement function for receiving seismic waves.

Claims

1. A deep-buried tunnel microseismic monitoring method based on a Transformer time series model, characterized in that, The method comprises: Step S1: obtaining microseismic monitoring signals based on the set monitoring section, and dividing the microseismic monitoring signals into different data frames according to the set window length and step length; Step S2: establishing a Transformer time sequence model based on a multi-head attention mechanism, wherein the multi-head attention mechanism of the Transformer time sequence model comprises a phase prior bias of a P-wave first arrival time obtained based on physical prior knowledge; The output layer of the Transformer time sequence model comprises an event category classification head, a microseismic event existence output head and a phase arrival time regression head, the event existence output head is used for outputting the probability of a microseismic event, the event category classification head is used for outputting the event category, and the phase arrival time regression head is used for outputting the predicted arrival time of a P-wave or an S-wave; The P-wave first arrival time is added to the Transformer time series model based on a multi-head attention mechanism to establish a biased attention weight matrix. This allows the model to determine the existence of microseismic event frames, the probability of microseismic events, and the prediction of P-waves or S-waves within the P-wave first arrival time range. The biased attention weight matrix is ​​as follows: , ,in, , , These are the query, key, and value matrices, respectively. For channel dimensions; The relative time error between the query and the key; For the index of the data frame; For the first The P-wave arrival time of each monitoring section; This is the tolerance for the P-wave first arrival time window; The bias strength; Step S3: training the Transformer time sequence model by taking the data frames as input, and predicting microseismic events based on the trained Transformer time sequence model; Step S4: merging and fusing the data frames determined as microseismic events to obtain the start and end time of the microseismic event; Step S5: based on the monitoring section position and the start and end time of the microseismic event, the improved particle swarm optimization algorithm is used to solve the microseismic event source position and the microseismic energy.

2. The deep-buried tunnel microseismic monitoring method based on the Transformer timing model according to claim 1, characterized in that, The monitoring section setting in step S1 comprises: setting a near-field monitoring section, a middle-field monitoring section and a far-field monitoring section behind the working face, obtaining microseismic monitoring signals based on the set three-level monitoring sections, the near-field monitoring section is 10-20 m away from the working face, the middle-field monitoring section is 30-50 m away from the working face, and the far-field monitoring section is 60-80 m away from the working face.

3. The deep-buried tunnel microseismic monitoring method based on the Transformer timing model according to claim 2, characterized in that, The step S1 comprises: arranging sensors on the top, bottom and left and right sides of the monitoring section, simultaneously adopting four groups of sensors to rotate in turn, and dynamically migrating the monitoring section according to the mode of removing the original far-field monitoring section, upgrading the near-field monitoring section to the middle-field monitoring section, upgrading the middle-field monitoring section to the far-field monitoring section, and arranging a new near-field monitoring section to obtain the microseismic monitoring signals.

4. The deep-buried tunnel microseismic monitoring method based on the Transformer timing model according to claim 1, characterized in that, The P-wave first arrival time in step S2 is obtained based on the ratio of short-time average to long-time average.

5. The deep-buried tunnel microseismic monitoring method based on the Transformer timing model according to claim 1, characterized in that, Step S3 of training the Transformer time sequence model comprises: fusion features including monitoring section positions and data frames are obtained through three-component channel attention fusion , the fusion features , time encoding and monitoring section position encoding are spliced as inputs to train a Transformer time sequence model established with true labels corresponding to whether an event exists in a data frame, an event category, and P-wave or S-wave arrival time; Based on a loss function during training Evaluate the model training results, optimize the model, the loss function is , ; wherein, , , and are weight coefficients; is binary cross entropy, used to determine whether a microseismic event occurs; is the true label, indicates the presence of an event, indicates the absence of an event; is the probability of the event predicted by the model, when there is an event is 1, otherwise is 0; is an indicator function, only on frames with events to calculate multi-class cross entropy; is the true label of the event type; is the event category index; is the probability distribution of the event type predicted by the model; is the Huber loss; and are the P-wave and S-wave arrival times predicted by the model; and are the true labels of P-wave and S-wave arrival times, respectively; is the safety phase interval, ; is the category traversal index in the summation formula; is the logit vector of the classification head; is the logit value of the th event; is the temperature parameter; is the total number of event categories.

6. The deep-buried tunnel microseismic monitoring method based on the Transformer timing model according to claim 1, characterized in that, Step S4 of merging and fusing the data frames determined as microseismic events comprises: Estimate dynamic noise with sliding window MAD and give threshold , When the microseismic event probability of a data frame is greater than , mark the data frame as a microseismic event frame, wherein, is the median; is the sliding window sequence for threshold estimation; is the noise scale estimation; is the sliding window mean; is the threshold coefficient; is the microseismic event threshold; Merge the continuous labeled microseismic event frames into complete microseismic events and calculate the sum classification probability of the microseismic events: , , where, is the set of data frames; is the data frame index; is the weighted integrated probability that the entire event belongs to class c; is the probability of the class ; is the weight of the frame; is the tuning parameter; is the probability that the data frame belongs to class c; is the signal-to-noise ratio of the data frame ; is the event class of the final output; is the confidence of the event.

7. The deep-buried tunnel microseismic monitoring method based on the Transformer timing model according to claim 1, characterized in that, The method for obtaining the position of the seismic source in step S6 is: for the confirmed microseismic event, a nonlinear equation set of the seismic source is constructed by using the time difference of the microseismic monitoring signal: , wherein, is the first microseismic signal monitoring position; is the position of the seismic source; is the first microseismic signal monitoring position; is the position of the seismic source; is the time when the microseismic signal is received by the first microseismic signal monitoring position; is the starting time of the microseismic event; is the propagation speed of the P wave; the nonlinear equation set of the seismic source is solved based on an improved particle swarm optimization algorithm, and the distance of the seismic source is obtained.

8. The deep-buried tunnel microseismic monitoring method based on the Transformer timing model according to claim 1, characterized in that, The objective function of the improved particle swarm optimization algorithm is wherein, is the start time of the microseismic event; is the time when the microseismic signal is received by the th microseismic signal monitoring position; represents the number of the microseismic signal monitoring position; is the total number of the microseismic signal monitoring positions.

9. The deep-buried tunnel microseismic monitoring method based on the Transformer timing model according to claim 1, characterized in that, Microseismic energy in step S6 is calculated in the following way: wherein, is the density of the surrounding rock; is the transmission speed of the microseismic monitoring signal; is the distance to the seismic source; is the time span of the microseismic monitoring signal; is the displacement function of the microseismic monitoring signal at the monitoring location of the microseismic signal.

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